gratefulphish, sorry to be late in replying, but I had an opera to record last night (yeah, I know, "excuses, excuses").
The confusion, I think, is between two angles which have a cause-and-effect relationship, but aren't the same thing:
(a) the physical angle between the main axes of a pair of microphones, and
(b) the arc of sound from the original venue which they cover (specified as an angle).
The second of these is what Prof. Williams calls the "stereophonic recording angle," and in general, the wider you make (a), the narrower (b) will be and vice versa. That's the big paradox that I referred to earlier.
Most people assume that the wider they spread their microphones, the wider an arc they will cover. It's as obvious as the observation that the Sun revolves around the Earth ... and just as wrong. The arc that you cover with a stereo pair of microphones (coincident or closely spaced directional microphones, anyway) corresponds more or less to the area of overlap between their polar patterns. The wider you spread them apart, the smaller this area of overlap will be, and thus the narrower the angle of stereo coverage will be.
Whenever a direct sound source is picked up exclusively (or nearly so) by just one of the two microphones, it will appear to come from the location of the corresponding loudspeaker during playback. Usually you only want (at most) the very farthest extreme sound sources to be reproduced that way; often it's preferable for not even the most extreme left and right sound sources seem to come from the location of either loudspeaker. You don't want to "advertise" the loudspeaker's exact position, because stereo sound is an illusion and an auditory awareness of the loudspeaker position tends to spoil that illusion.
You want (this being an esthetic convention, i.e. something subjective that is nonetheless advisable because it's the generally accepted paradigm) the direct sound to be spread across "an appropriate amount" of the space between the loudspeakers, depending on how wide the original direct sound source was. A solo piccolo shouldn't fill the entire soundstage width, and actually neither should a solo piano, even if it's one of those huge, long Bösendorfer concert grands. Your choice of the microphone patterns and geometry (angle and distance between mikes, and distance from mikes to sound sources) determines the audibly "apparent" width (what the Germans call the "stereo basis width") that will be produced later over loudspeakers.
--best regards